Finite Group Databasebeta

← C31×#10361 #21467120

Subgroups — C31×#10361 #21467120

Order 7936.

392 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2845C211yesmaximal, characteristic
2C31×#1993C212yesmaximal
3C31×#1960C211yesmaximal, characteristic
4C31×#1295C212yesmaximal
5C31×#1295C211yesmaximal, characteristic
6C2×C31×C4⋊Q8C2211yescharacteristic
7C2×C31×#103—22no—
8C2×C31×#97C2211yescharacteristic
9C2×C31×#97C2212yes—
10C31×#398—22no—
11C31×#398—22no—
12C31×#398—22no—
13C31×#382C2211yescharacteristic
14C31×#382C2212yes—
15C31×#340—22no—
16C31×#340—22no—
17C22×Q8×C31—21no—
18C22×C8×C31—21no—
19C22×C8×C31—22no—
20C31×C4⋊Q8—22no—
21C31×C4⋊Q8—21no—
22C31×C4⋊Q8Q812yes—
23C2×C4⋊C4×C31—22no—
24C2×C4⋊C4×C31—22no—
25C2×C4⋊C4×C31—22no—
26C2×C4⋊C4×C31—22no—
27C2×C4⋊C4×C31D412yes—
28C2×C4⋊C4×C31D412yes—
29C2×C4⋊C4×C31D412yes—
30C2×C42×C31C2311yescharacteristic
31C31×#103—44no—
32C31×#97—22no—
33C31×#97—22no—
34C31×#97—22no—
35C31×#95—22no—
36C31×#95—22no—
37C31×#95—22no—
38C31×#95—22no—
39C2×Q8×C31—22no—
40C2×Q8×C31—42no—
41C2×Q8×C31—42no—
42C2×Q8×C31—41no—
43C22×C4×C31—22no—
44C22×C4×C31—22no—
45C22×C4×C31—22no—
46C22×C4×C31—41no—
47C22×C4×C31C2×D412yes—
48C22×C4×C31C2×D411yescharacteristic
49C2×C8×C31—22no—
50C2×C8×C31—24no—
51C2×C8×C31—41no—
52C2×C8×C31—42no—
53C2×C8×C31—42no—
54C2×C8×C31—41no—
55C4⋊C4×C31—24no—
56C4⋊C4×C31—42no—
57C4⋊C4×C31—42no—
58C4⋊C4×C31—42no—
59C4⋊C4×C31—42no—
60C4⋊C4×C31—82no—
61C4⋊C4×C31—82no—
62C4⋊C4×C31—82no—
63C42×C31C2×Q811yescharacteristic
64C42×C31#4112yes—
65C42×C31#4111yescharacteristic
66#10361C3111yesmaximal, characteristic, direct product factor, Sylow
67C23×C31#12011yescharacteristic
68Q8×C31—44no—
69Q8×C31—82no—
70C2×C4×C31—21no—
71C2×C4×C31—21no—
72C2×C4×C31—22no—
73C2×C4×C31—22no—
74C2×C4×C31—42no—
75C2×C4×C31—42no—
76C2×C4×C31—42no—
77C2×C4×C31—42no—
78C2×C4×C31—42no—
79C2×C4×C31—42no—
80C2×C4×C31—42no—
81C2×C4×C31—42no—
82C2×C4×C31—42no—
83C2×C4×C31—42no—
84C2×C4×C31—81no—
85C2×C4×C31—81no—
86C2×C4×C31C22⋊Q812yes—
87C2×C4×C31C22⋊Q811yescharacteristic
88C2×C4×C31#12412yes—
89C2×C4×C31#12411yescharacteristic
90C8×C31—42no—
91C8×C31—44no—
92#2845C2×C3111yescharacteristic
93#1993C2×C3112yes—
94#1960C2×C3111yescharacteristic
95#1295C2×C3111yescharacteristic
96#1295C2×C3112yes—
97C22×C31#39311yescharacteristic
98C22×C31#45311yescharacteristic
99C22×C31#45411yescharacteristic
100C22×C31#45512yes—
101C22×C31#45612yes—
102C4×C31—21no—
103C4×C31—21no—
104C4×C31—22no—
105C4×C31—22no—
106C4×C31—82no—
107C4×C31—82no—
108C4×C31—82no—
109C4×C31—82no—
110C2×C4⋊Q8C22×C3111yescharacteristic
111C2×#103—22no—
112C2×#97C22×C3111yescharacteristic
113C2×#97C22×C3112yes—
114#398—22no—
115#398—22no—
116#398—22no—
117#382C22×C3111yescharacteristic
118#382C22×C3112yes—
119#340—22no—
120#340—22no—
121C2×C31#166112yes—
122C2×C31#166211yescharacteristic
123C2×C31#166311yescharacteristic
124C2×C31#202711yescharacteristic
125C2×C31#202812yes—
126C22×Q8—21no—
127C22×C8—22no—
128C22×C8—21no—
129C4⋊Q8—22no—
130C4⋊Q8—21no—
131C4⋊Q8Q8×C3112yes—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4D4×C3112yes—
137C2×C4⋊C4D4×C3112yes—
138C2×C4⋊C4D4×C3112yes—
139C2×C42C23×C3111yescharacteristic
140#103—44no—
141#97—22no—
142#97—22no—
143#97—22no—
144#95—22no—
145#95—22no—
146#95—22no—
147#95—22no—
148C31#1036111yescharacteristic, direct product factor, Sylow
149C2×Q8—22no—
150C2×Q8—42no—
151C2×Q8—42no—
152C2×Q8—41no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—41no—
157C22×C4C2×D4×C3112yes—
158C22×C4C2×D4×C3111yescharacteristic
159C2×C8—22no—
160C2×C8—24no—
161C2×C8—41no—
162C2×C8—42no—
163C2×C8—42no—
164C2×C8—41no—
165C4⋊C4—24no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—42no—
170C4⋊C4—82no—
171C4⋊C4—82no—
172C4⋊C4—82no—
173C42C2×Q8×C3111yescharacteristic
174C42#41×C3112yes—
175C42#41×C3111yescharacteristic
176C23C31×#12011yescharacteristic
177Q8—44no—
178Q8—82no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—81no—
194C2×C4—81no—
195C2×C4C31×C22⋊Q812yes—
196C2×C4C31×C22⋊Q811yescharacteristic
197C2×C4C31×#12412yes—
198C2×C4C31×#12411yescharacteristic
199C8—42no—
200C8—44no—
201C22C31×#39311yescharacteristic
202C22C31×#45311yescharacteristic
203C22C31×#45411yescharacteristic
204C22C31×#45512yes—
205C22C31×#45612yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—82no—
212C4—82no—
213C4—82no—
214C2C31×#166112yes—
215C2C31×#166211yescharacteristic
216C2C31×#166311yescharacteristic
217C2C31×#202711yescharacteristic
218C2C31×#202812yes—
subgroupG/H
center, socle, prime radicalC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
66. #10361C31direct (N × H)
148. C31#10361direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C31×#28452
C31×#19932
C31×#19602
C31×#12952
#1036131